{ "cells": [ { "cell_type": "markdown", "id": "f53f2418", "metadata": {}, "source": [ "# Bracketing Method\n", "**강좌**: *수치해석*" ] }, { "cell_type": "markdown", "id": "83e2f29d", "metadata": {}, "source": [ "## 그래프를 이용한 방정식 해 찾기\n", "[낙하산병 문제](../contents/Lecture_01_Exercise_101.ipynb) 에서 아래를 상황을 생각해보자.\n", "\n", "질량 $m=68.1kg$인 낙하산병이 자유낙하할 때 10초 후 속도가 $40m/s$ 가 되는 항력 계수는 얼마인가?\n", "\n", "엄밀해를 이용하면 다음과 같다.\n", "\n", "$$\n", "f(c)= \\frac{mg}{c} (1 - e^{(-c/m)t}) - 40 = \\frac{9.81(68.1)}{c} (1 - e^{(-c/68.1)10})\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "id": "061afab9", "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "from matplotlib import pyplot as plt\n", "\n", "import numpy as np\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.dpi'] = 150" ] }, { "cell_type": "code", "execution_count": 2, "id": "66039494", "metadata": {}, "outputs": [], "source": [ "# 주요 상수\n", "m = 68.1\n", "g = 9.81\n", "t = 10\n", "\n", "\n", "def f(c):\n", " # using the exact solution\n", " return m*g/c*(1 - np.exp(-c/m*t)) - 40" ] }, { "cell_type": "code", "execution_count": 3, "id": "e5d42094", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4 34.19047156669296\n", "8 17.712257537470236\n", "12 6.113943075921462\n", "16 -2.230260706051183\n", "20 -8.368384465361824\n" ] } ], "source": [ "# 4~20 사이에서 값 계산\n", "for c in range(4, 21, 4):\n", " print(c, f(c))" ] }, { "cell_type": "code", "execution_count": 4, "id": "11a1a0e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 초기 Guess (0, 20)\n", "c = np.linspace(1, 20, 101)\n", "\n", "# Plot\n", "plt.plot(c, f(c))\n", "\n", "# From graph\n", "plt.plot(14.75, f(14.75), marker='x')\n", "\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "markdown", "id": "647f1287", "metadata": {}, "source": [ "## Bisection Method\n", "그래프로 구하는 과정을 체계적으로 생각해보면, 구간을 정하고 양 끝 점에서 부호가 같은지 다른지 확인하고 구간을 줄여 나간다.\n", "\n", "$$\n", "f(a)\\times f(b) < 0\n", "$$\n", "\n", "### 알고리즘\n", "* 해가 구간 (a, b) 사이에 있을 때 해가 존재하면 $f(a)\\cdot f(b) < 0$ 조건을 활용한다.\n", "\n", "* 이 경우 중간 값 $c=\\frac{a+b}{2}$ 에 대해 \n", "\n", " * $f(a)\\cdot f(c) < 0$ 이면 해가 (a, c) 사이에 있다고 범위를 좁힘\n", " \n", " * $f(c)\\cdot f(b) < 0$ 이면 해가 (c, b) 사이에 있다고 범위를 좁힘\n", "\n", ":::{figure-md} markdown-fig\n", "\"bisect-fig\"\n", "\n", "Bisection method (From Wikipedia)\n", ":::" ] }, { "cell_type": "markdown", "id": "463ea597", "metadata": {}, "source": [ "### By hand\n", "첫번째 구간을 [12, 16] 으로 한 후 진행해보자" ] }, { "cell_type": "code", "execution_count": 5, "id": "aa45d3e9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a, b = 12, 16\n", "\n", "# Check if the solution lies within the interval [a, b]\n", "f(a)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 6, "id": "f50bac58", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(False, True)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 7, "id": "77550ae6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.0, 16)\n" ] } ], "source": [ "# 범위를 좁힘\n", "a = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 8, "id": "638c9b78", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(True, False)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 9, "id": "b4f4aaae", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.0, 15.0)\n" ] } ], "source": [ "# 범위를 좁힘\n", "b = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 10, "id": "9cf48ef3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(False, True)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 11, "id": "1131eedf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.5, 15.0)\n" ] } ], "source": [ "# 범위를 좁힘\n", "a = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 12, "id": "81915125", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(False, True)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 13, "id": "e86ed401", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.75, 15.0)\n" ] } ], "source": [ "# 범위를 좁힘\n", "a = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 14, "id": "9a4cd2a5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(True, False)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 15, "id": "2bb36b7e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.75, 14.875)\n" ] } ], "source": [ "# 범위를 좁힘\n", "b = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 16, "id": "ac49f4b0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(True, False)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 17, "id": "c7ec330c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.75, 14.8125)\n" ] } ], "source": [ "# 범위를 좁힘\n", "b = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 18, "id": "4621bc85", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(False, True)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "code", "execution_count": 19, "id": "f26a0e49", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "New interval: (14.78125, 14.8125)\n" ] } ], "source": [ "# 범위를 좁힘\n", "a = c\n", "print(\"New interval: {}\".format((a, b)))" ] }, { "cell_type": "code", "execution_count": 20, "id": "ca38a6ec", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(False, True)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Midpoint\n", "c = 0.5*(a + b)\n", "\n", "# 해가 [a, c]. [c, b] 중 어디에 존재하는지 확인\n", "f(a)*f(c) < 0, f(c)*f(b) < 0" ] }, { "cell_type": "markdown", "id": "8a5d0d13", "metadata": {}, "source": [ "#### 종료 판정 기준\n", "위 과정은 무한히 계속될 수 있다. 적당한 해상도 이내에서 계산이 되었으면 멈춰야 한다.\n", "\n", "즉 오차가 일정 수준 이내, 상대 오차가 일정 수준 이내이면 멈추기로 한다.\n", "\n", "엄밀해를 모르므로 근사 상대 오차 $\\epsilon_a$ 의 크기가 $tol$ 보다 작으면 멈춘다.\n", "\n", " \n", ":::{note}\n", "$\\epsilon_a< tol$ 이면 멈춘다.\n", ":::" ] }, { "cell_type": "markdown", "id": "fc5a6617", "metadata": {}, "source": [ "### Make a code\n", "`if` 구문으로 어떤 쪽으로 선택할 지 만들어 본다." ] }, { "cell_type": "code", "execution_count": 21, "id": "e94ff849", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 14.0 16 15.0\n", "1 14.0 15.0 14.5\n", "2 14.5 15.0 14.75\n", "3 14.75 15.0 14.875\n", "4 14.75 14.875 14.8125\n", "5 14.75 14.8125 14.78125\n", "6 14.78125 14.8125 14.796875\n", "7 14.796875 14.8125 14.8046875\n", "8 14.796875 14.8046875 14.80078125\n", "9 14.80078125 14.8046875 14.802734375\n", "10 14.80078125 14.802734375 14.8017578125\n", "11 14.80078125 14.8017578125 14.80126953125\n", "12 14.80078125 14.80126953125 14.801025390625\n", "13 14.801025390625 14.80126953125 14.8011474609375\n", "14 14.801025390625 14.8011474609375 14.80108642578125\n", "15 14.80108642578125 14.8011474609375 14.801116943359375\n", "16 14.801116943359375 14.8011474609375 14.801132202148438\n", "Converged at 14.801139831542969\n" ] } ], "source": [ "a, b = 12, 16\n", "c = 0.5*(a+b)\n", "\n", "iter_max = 20\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = 0.5*(a + b)\n", " \n", " # Compute relative error\n", " if abs((c0 - c)/c) < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c)" ] }, { "cell_type": "markdown", "id": "406c917c", "metadata": {}, "source": [ "엄밀해가 $c = 14.8011$ 임을 이용해서 상대오차를 구해보자." ] }, { "cell_type": "code", "execution_count": 22, "id": "89db4bee", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 14.0 16 15.0 0.013260000000000004 0.06666666666666667\n", "1 14.0 15.0 14.5 0.020765517241379306 0.034482758620689655\n", "2 14.5 15.0 14.75 0.0034644067796610117 0.01694915254237288\n", "3 14.75 15.0 14.875 0.004968067226890762 0.008403361344537815\n", "4 14.75 14.875 14.8125 0.0007696202531645622 0.004219409282700422\n", "5 14.75 14.8125 14.78125 0.0013429175475687051 0.0021141649048625794\n", "6 14.78125 14.8125 14.796875 0.0002855332629355809 0.0010559662090813093\n", "7 14.796875 14.8125 14.8046875 0.00024232189973615295 0.0005277044854881266\n", "8 14.796875 14.8046875 14.80078125 2.1536025336495212e-05 0.0002639218791237794\n", "9 14.80078125 14.8046875 14.802734375 0.00011041034437261371 0.00013194352816994325\n", "10 14.80078125 14.802734375 14.8017578125 4.444151217259871e-05 6.597611664577422e-05\n", "11 14.80078125 14.8017578125 14.80126953125 1.145383168937938e-05 3.298914657077821e-05\n", "12 14.80078125 14.80126953125 14.801025390625 5.040824742262857e-06 1.6494845360824743e-05\n", "13 14.801025390625 14.80126953125 14.8011474609375 3.2065714921990636e-06 8.247354660992487e-06\n", "14 14.801025390625 14.8011474609375 14.80108642578125 9.171096201613302e-07 4.123694335281092e-06\n", "15 14.80108642578125 14.8011474609375 14.801116943359375 1.1447351872102123e-06 2.0618429164355686e-06\n", "16 14.801116943359375 14.8011474609375 14.801132202148438 2.175654402499187e-06 1.030920395419827e-06\n", "Converged at 14.801139831542969\n" ] } ], "source": [ "a, b = 12, 16\n", "c = 0.5*(a+b)\n", "\n", "c_ex = 14.8011\n", "\n", "# 상대오차 (참, 근사)\n", "eps_t = []\n", "eps_a = []\n", "\n", "iter_max = 20\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = 0.5*(a + b)\n", " \n", " # Compute relative error\n", " eps_ti = abs((c - c_ex)/c)\n", " eps_ai = abs((c0 - c)/c)\n", " eps_t.append(eps_ti)\n", " eps_a.append(eps_ai)\n", " \n", " if eps_ai < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c, eps_ti, eps_ai)" ] }, { "cell_type": "code", "execution_count": 23, "id": "7b54a9e4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Error')" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(eps_t)\n", "plt.semilogy(eps_a)\n", "\n", "plt.legend(['True', 'Approximation'])\n", "plt.xlabel('Iter')\n", "plt.ylabel('Error')" ] }, { "cell_type": "markdown", "id": "f6815cab", "metadata": {}, "source": [ "- Bisection method를 진행하면서 오차의 범위가 절반씩 줄어든다." ] }, { "cell_type": "markdown", "id": "19fa81cb", "metadata": {}, "source": [ "#### Recursive algorithm\n", "\n", "함수 안에서 함수를 호출\n", "\n", ":::{figure-md} Recursive-algorihm\n", "\"recursiv-fig\"\n", "\n", "Recursive algorihm (From Wikipedia)\n", ":::\n", "\n", ":::{note}\n", "$\\epsilon_a$ 계산시 $c=0$ 일 때 분모가 0이 될 수 있다. 분모에 매우 작은 값을 더하자.\n", ":::" ] }, { "cell_type": "code", "execution_count": 24, "id": "861d1cf0", "metadata": {}, "outputs": [], "source": [ "def bisect(a, b, f, c0=a, tol=1e-6):\n", " \"\"\"\n", " Bisection method\n", " \n", " Parameters\n", " ----------\n", " a : float\n", " Lower limit\n", " b : float\n", " Upper limit\n", " c0 : float\n", " Previous solution\n", " f : function\n", " 함수\n", " tol : float\n", " Tolerance\n", " \"\"\"\n", " fa, fb = f(a), f(b)\n", " product = fa*fb\n", "\n", " # 구간 경계에서 해가 존재한 경우\n", " if product == 0:\n", " if fa == 0:\n", " print('Converged at {:.7g}'.format(a))\n", " \n", " return a\n", " else:\n", " print('Converged at {:.7g}'.format(b)) \n", " \n", " return b\n", " \n", " elif product > 0:\n", " # 같은 부호 이므로 이 구간 내에 해가 존재하지 않음\n", " raise ValueError('Wrong Intervals')\n", " \n", " else:\n", " c = 0.5*(a+b)\n", " \n", " # Convergence 조건\n", " if (abs(c - c0)/ max(abs(c), tol)) < tol:\n", " print('Converged at {:.7g}'.format(c))\n", " \n", " return c\n", " elif fa*f(c) < 0:\n", " # 해는 (a,c) 사이에 존재함, 범위 좁히기\n", " bisect(a, c, f, c, tol)\n", " else:\n", " # 해는 (c,a) 사이에 존재함, 범위 좁히기\n", " bisect(c, b, f, c, tol)" ] }, { "cell_type": "code", "execution_count": 25, "id": "4f0341c0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Converged at 14.80114\n" ] } ], "source": [ "bisect(12, 16, f)" ] }, { "cell_type": "markdown", "id": "3041e8f2", "metadata": {}, "source": [ "### 구간 설정\n", "- Bracketing method는 적절한 구간 설정이 중요함\n", "- 1개의 해를 포함하는 구간을 설정해야 함" ] }, { "cell_type": "code", "execution_count": 26, "id": "2ab1eeb5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(-10, 10, 0.1)\n", "\n", "def f1(x):\n", " return x**2 + 10*np.sin(x)\n", "\n", "plt.plot(x, f1(x))\n", "plt.xlabel('x')\n", "plt.ylabel('y')\n", "plt.legend([\"$x^2 + 10\\sin(x)$\"])" ] }, { "cell_type": "code", "execution_count": 27, "id": "d582c2e7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Converged at -2.479483\n" ] } ], "source": [ "# Left solution\n", "bisect(-10, -1, f1)" ] }, { "cell_type": "code", "execution_count": 28, "id": "b6b4140e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1(0)" ] }, { "cell_type": "code", "execution_count": 29, "id": "6e5b1a93", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Converged at 0\n" ] } ], "source": [ "# Right solution\n", "bisect(-1, 1, f1)" ] }, { "cell_type": "code", "execution_count": 30, "id": "bf9e4b46", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "Wrong Intervals", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn [30], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;66;03m# Wrong Interval 1\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[43mbisect\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m10\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf1\u001b[49m\u001b[43m)\u001b[49m\n", "Cell \u001b[0;32mIn [24], line 34\u001b[0m, in \u001b[0;36mbisect\u001b[0;34m(a, b, f, c0, tol)\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m b\n\u001b[1;32m 32\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m product \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[1;32m 33\u001b[0m \u001b[38;5;66;03m# 같은 부호 이므로 이 구간 내에 해가 존재하지 않음\u001b[39;00m\n\u001b[0;32m---> 34\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mWrong Intervals\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 36\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 37\u001b[0m c \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.5\u001b[39m\u001b[38;5;241m*\u001b[39m(a\u001b[38;5;241m+\u001b[39mb)\n", "\u001b[0;31mValueError\u001b[0m: Wrong Intervals" ] } ], "source": [ "# Wrong Interval 1\n", "bisect(-10, -5, f1)" ] }, { "cell_type": "code", "execution_count": 31, "id": "cf758380", "metadata": {}, "outputs": [ { "ename": "ValueError", "evalue": "Wrong Intervals", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn [31], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;66;03m# Wrong Interval 2\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[43mbisect\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf1\u001b[49m\u001b[43m)\u001b[49m\n", "Cell \u001b[0;32mIn [24], line 34\u001b[0m, in \u001b[0;36mbisect\u001b[0;34m(a, b, f, c0, tol)\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m b\n\u001b[1;32m 32\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m product \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m0\u001b[39m:\n\u001b[1;32m 33\u001b[0m \u001b[38;5;66;03m# 같은 부호 이므로 이 구간 내에 해가 존재하지 않음\u001b[39;00m\n\u001b[0;32m---> 34\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mWrong Intervals\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 36\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 37\u001b[0m c \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.5\u001b[39m\u001b[38;5;241m*\u001b[39m(a\u001b[38;5;241m+\u001b[39mb)\n", "\u001b[0;31mValueError\u001b[0m: Wrong Intervals" ] } ], "source": [ "# Wrong Interval 2\n", "bisect(-5, 5, f1)" ] }, { "cell_type": "markdown", "id": "daab9bc2", "metadata": {}, "source": [ "### DIY\n", "`For-Loop` 를 이용하여 Bisection method 계산 함수를 만드시오. 아래 기능도 같이 구현하시오.\n", "- boolean 형식의 *verbose* keyword argument를 추가하라.\n", " * True 일 경우 중간 계산 결과 및 상대 오차를 출력한다.\n", " * False 일 경우 최종 해만 출력한다.\n", " * 기본 값은 False로 한다." ] }, { "cell_type": "markdown", "id": "3ec61587", "metadata": {}, "source": [ "## Method of False Position\n", "\n", "Bisection method 보다 계산 효율을 높이기 위해 가 위치 (False position)를 사용한다.\n", "\n", "이 위치는 중점 대신에 양 끝점을 직선으로 이었을 때 교점을 사용한다.\n", "\n", "아래 그림을 보면 다음 관계로 가 위치를 구한다.\n", "\n", "$$\n", "\\frac{f(a)}{c - a} = \\frac{f(b)}{c - b}\n", "$$\n", "\n", "이를 정리하면 다음과 같다.\n", "\n", "$$\n", "c = \\frac{b f(a) - a f(b)} {f(a) - f(b)} = b - \\frac{f(b)(a-b)}{f(a) - f(b)}\n", "$$\n", "\n", ":::{figure-md} false-pos-fig\n", "\"false-pos-fig\"\n", "\n", "Method of false position (From Wikimedia)\n", ":::\n", "\n", "### 알고리즘\n", "* 해가 구간 (a, b) 사이에 있을 때 해가 존재하면 $f(a)\\cdot f(b) < 0$ 조건을 활용한다.\n", "\n", "* 이 경우 중간 값 $c=b - \\frac{f(b)(a-b)}{f(a) - f(b)}$ 에 대해 \n", "\n", " * $f(a)\\cdot f(c) < 0$ 이면 해가 (a, c) 사이에 있다고 범위를 좁힘\n", " \n", " * $f(c)\\cdot f(b) < 0$ 이면 해가 (c, b) 사이에 있다고 범위를 좁힘" ] }, { "cell_type": "code", "execution_count": 32, "id": "8e9ad65d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 12 14.930869492487908 14.815076015455954 0.0009433644107781617 0.007815921896799652\n", "1 12 14.815076015455954 14.802632653525668 0.00010353925288440446 0.0008406181671557055\n", "2 12 14.802632653525668 14.80129662906239 1.328458359549417e-05 9.026401515760205e-05\n", "3 12 14.80129662906239 14.801153195602156 3.594017402097734e-06 9.690694930243335e-06\n", "4 12 14.801153195602156 14.801137796968773 2.5536529212191533e-06 1.040368219980068e-06\n", "Converged at 14.801136143814386\n" ] } ], "source": [ "a, b = 12, 16\n", "c = b - f(b)*(a-b)/(f(a) - f(b))\n", "\n", "c_ex = 14.8011\n", "\n", "# 상대오차 (참, 근사)\n", "eps_t = []\n", "eps_a = []\n", "\n", "iter_max = 20\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = b - f(b)*(a-b)/(f(a) - f(b))\n", " \n", " # Compute relative error\n", " eps_ti = abs((c - c_ex)/c)\n", " eps_ai = abs((c0 - c)/c)\n", " eps_t.append(eps_ti)\n", " eps_a.append(eps_ai)\n", " \n", " if eps_ai < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c, eps_ti, eps_ai)" ] }, { "cell_type": "code", "execution_count": 33, "id": "94df57e6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Error')" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(eps_t)\n", "plt.semilogy(eps_a)\n", "\n", "plt.legend(['True', 'Approximation'])\n", "plt.xlabel('Iter')\n", "plt.ylabel('Error')" ] }, { "cell_type": "markdown", "id": "11fd96cc", "metadata": {}, "source": [ "### DIY\n", "Method of False Position 함수를 `For-loop` 버전과 `Recursive algorithm` 버전으로 완성하시오." ] }, { "cell_type": "markdown", "id": "ca1ecaf1", "metadata": {}, "source": [ "### 문제점\n", "- 곡률이 큰 함수에서 수렴이 매우 느릴 수 있다.\n", "\n", "x 가 $[0, 1.3]$ 사이일 때 아래 함수의 해를 구하시오.\n", "\n", "$$\n", "f(x) = x^{10} - 1\n", "$$" ] }, { "cell_type": "code", "execution_count": 34, "id": "22a9a685", "metadata": {}, "outputs": [], "source": [ "# 함수 정의\n", "f = lambda x : x**10 - 1" ] }, { "cell_type": "code", "execution_count": 35, "id": "53a472c0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1.3, 131)\n", "\n", "plt.plot(x, f(x))\n", "plt.plot([1], [0], marker='x')\n", "\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": 36, "id": "7240b968", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0.65 1.3 0.9750000000000001 0.025641025641025546 0.33333333333333337\n", "1 0.9750000000000001 1.3 1.1375000000000002 0.12087912087912102 0.1428571428571429\n", "2 0.9750000000000001 1.1375000000000002 1.0562500000000001 0.053254437869822605 0.07692307692307696\n", "3 0.9750000000000001 1.0562500000000001 1.015625 0.015384615384615385 0.04000000000000013\n", "4 0.9750000000000001 1.015625 0.9953125 0.004709576138147522 0.020408163265306076\n", "5 0.9953125 1.015625 1.00546875 0.005439005439005351 0.01010101010100997\n", "6 0.9953125 1.00546875 1.000390625 0.00039047247169083456 0.005076142131979517\n", "7 0.9953125 1.000390625 0.9978515625000001 0.0021530632217654447 0.002544529262086536\n", "8 0.9978515625000001 1.000390625 0.9991210937500001 0.0008796794057275569 0.0012706480304956191\n", "9 0.9991210937500001 1.000390625 0.9997558593750001 0.0002442002442001331 0.0006349206349206127\n", "10 0.9997558593750001 1.000390625 1.0000732421875 7.323682347488755e-05 0.00031735956839092034\n", "11 0.9997558593750001 1.0000732421875 0.9999145507812501 8.545652094281841e-05 0.00015870496746539284\n", "12 0.9999145507812501 1.0000732421875 0.9999938964843751 6.103552878041541e-06 7.934618741565026e-05\n", "13 0.9999938964843751 1.0000732421875 1.0000335693359377 3.356820907519036e-05 3.9671519816012954e-05\n", "14 0.9999938964843751 1.0000335693359377 1.0000137329101564 1.3732721566151756e-05 1.9836153373182286e-05\n", "15 0.9999938964843751 1.0000137329101564 1.0000038146972656 3.8146827137652828e-06 9.918175055922961e-06\n", "16 0.9999938964843751 1.0000038146972656 0.9999988555908204 1.1444104893169604e-06 4.9591121205215245e-06\n", "17 0.9999988555908204 1.0000038146972656 1.0000013351440429 1.3351422602726969e-06 2.4795499119667293e-06\n", "18 0.9999988555908204 1.0000013351440429 1.0000000953674317 9.536742263449668e-08 1.2397764929161892e-06\n", "Converged at 0.999999475479126\n" ] } ], "source": [ "a, b = 0, 1.3\n", "c = 0.5*(a+b)\n", "\n", "c_ex = 1\n", "\n", "# 상대오차 (참, 근사)\n", "eps_t = []\n", "eps_a = []\n", "\n", "# 해석 결과\n", "cs = []\n", "\n", "iter_max = 25\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = 0.5*(a + b)\n", " cs.append(c)\n", " \n", " # Compute relative error\n", " eps_ti = abs((c - c_ex)/c)\n", " eps_ai = abs((c0 - c)/c)\n", " eps_t.append(eps_ti)\n", " eps_a.append(eps_ai)\n", " \n", " if eps_ai < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c, eps_ti, eps_ai)" ] }, { "cell_type": "code", "execution_count": 37, "id": "e3422934", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1.3, 131)\n", "\n", "plt.plot(x, f(x))\n", "plt.plot(cs, np.zeros_like(cs), marker='x')\n", "\n", "plt.legend([\"$x^{10} -1$\", 'Bisection method'])\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": 38, "id": "84e50b43", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Error')" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(eps_t)\n", "plt.semilogy(eps_a)\n", "\n", "plt.legend(['True', 'Approximation'])\n", "plt.xlabel('Iter')\n", "plt.ylabel('Error')" ] }, { "cell_type": "code", "execution_count": 39, "id": "3038f3bd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 0.09429959537232735 1.3 0.1817588725190793 4.501794691728348 0.48118298674839827\n", "1 0.1817588725190793 1.3 0.2628740125203042 2.804103686068096 0.3085704030745893\n", "2 0.2628740125203042 1.3 0.3381051033222693 1.9576601777786151 0.22250800139581925\n", "3 0.3381051033222693 1.3 0.4078779165927523 1.4517140039195966 0.17106298338811027\n", "4 0.4078779165927523 1.3 0.4725831535623899 1.116029724000691 0.13691820472626154\n", "5 0.4725831535623899 1.3 0.5325715106320141 0.8776821141132359 0.11263906512467173\n", "6 0.5325715106320141 1.3 0.5881445691706797 0.7002622355419552 0.09448877274685547\n", "7 0.5881445691706797 1.3 0.6395439707682155 0.5636141464969289 0.08036883145938375\n", "8 0.6395439707682155 1.3 0.6869431667412387 0.45572450300926454 0.06900017100086796\n", "9 0.6869431667412387 1.3 0.7304464366929376 0.3690257762464468 0.05955709791488338\n", "10 0.7304464366929376 1.3 0.7700987444968072 0.29853477511304527 0.05148990059681097\n", "11 0.7700987444968072 1.3 0.8059075090169237 0.24083717897086934 0.044432846349573514\n", "12 0.8059075090169237 1.3 0.8378738914244523 0.19349702889049372 0.03815178242776284\n", "13 0.8378738914244523 1.3 0.8660276320873558 0.15469756731633996 0.03250905585430972\n", "14 0.8660276320873558 1.3 0.8904572813509997 0.12301849953183873 0.02743494806014644\n", "15 0.8904572813509997 1.3 0.9113282513082279 0.09729946214712669 0.022901704108555406\n", "16 0.9113282513082279 1.3 0.9288846695992142 0.07655991397884723 0.01890053616512088\n", "17 0.9288846695992142 1.3 0.9434360517492835 0.05995525414344491 0.015423813965015026\n", "18 0.9434360517492835 1.3 0.955333975192147 0.04675435603435884 0.012454203191580743\n", "19 0.955333975192147 1.3 0.9649455723416893 0.03632788072517092 0.009960766104369261\n", "20 0.9649455723416893 1.3 0.9726296888054463 0.028140526152526824 0.007900351544064411\n", "21 0.9726296888054463 1.3 0.9787191336334623 0.02174358877355671 0.00622185121221563\n", "22 0.9787191336334623 1.3 0.9835099523268419 0.01676652852789647 0.004871144091674134\n", "23 0.9835099523268419 1.3 0.9872569173655359 0.012907564799311435 0.0037953292327316803\n", "24 0.9872569173655359 1.3 0.9901736307394302 0.00992388501926856 0.0029456585020510096\n" ] } ], "source": [ "a, b = 0, 1.3\n", "c = b - f(b)*(a-b)/(f(a) - f(b))\n", "\n", "c_ex = 1\n", "\n", "# 상대오차 (참, 근사)\n", "eps_t = []\n", "eps_a = []\n", "\n", "# 해석 결과\n", "cs = []\n", "\n", "iter_max = 25\n", "for i in range(iter_max):\n", " if f(a)*f(c) < 0:\n", " b = c\n", " elif f(b)*f(c) < 0:\n", " a = c\n", "\n", " # Save old midpoint\n", " c0 = c\n", " \n", " # Compute new midpoint\n", " c = b - f(b)*(a-b)/(f(a) - f(b))\n", " cs.append(c)\n", " \n", " # Compute relative error\n", " eps_ti = abs((c - c_ex)/c)\n", " eps_ai = abs((c0 - c)/c)\n", " eps_t.append(eps_ti)\n", " eps_a.append(eps_ai)\n", " \n", " if eps_ai < 1e-6:\n", " # Stop and write converged solution\n", " print(\"Converged at {}\".format(c))\n", " break\n", " else:\n", " print(i, a, b, c, eps_ti, eps_ai)" ] }, { "cell_type": "code", "execution_count": 40, "id": "4a3d23ea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1.3, 131)\n", "\n", "plt.plot(x, f(x))\n", "plt.plot(cs, np.zeros_like(cs), marker='x')\n", "\n", "plt.legend([\"$x^{10} -1$\", 'Method of False Position'])\n", "plt.xlabel('x')\n", "plt.ylabel('y')" ] }, { "cell_type": "code", "execution_count": 41, "id": "bab4a0f9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Error')" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.semilogy(eps_t)\n", "plt.semilogy(eps_a)\n", "\n", "plt.legend(['True', 'Approximation'])\n", "plt.xlabel('Iter')\n", "plt.ylabel('Error')" ] }, { "cell_type": "markdown", "id": "11779255", "metadata": {}, "source": [ "## SciPy 활용\n", "`scipy.optimize` 모듈은 최소화, Curve fitting 그리고 root finding과 관련된 다양한 알고리듬을 제공한다.\n", "\n", "**참고**\n", "* https://scipy-lectures.org/intro/scipy.html#optimization-and-fit-scipy-optimize\n", "* https://docs.scipy.org/doc/scipy/reference/optimize.html" ] }, { "cell_type": "code", "execution_count": 42, "id": "ec4f3ef8", "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import root_scalar\n", "# root_scalar?" ] }, { "cell_type": "code", "execution_count": 43, "id": "f866698c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " converged: True\n", " flag: 'converged'\n", " function_calls: 10\n", " iterations: 9\n", " root: 0.9999999999998475" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "root_scalar(f, bracket=[0, 1.3])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }